Question

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 chevrolet cavalier states that the mean is 8.4 hours with standard deviation 1.8 hours. if 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.6 hours

Answer 1

The probability that their mean rebuild time exceeds at 8.7 hours is;z(8.7) = (8.7-8.4)/[1.8/sqrt(40)] = 1.0541
P(x-bar > 8.7) = P(z > 1.0541) = normal cdf (1.0541,100) = 0.1459
If 40 mechanics are randomly selected, the probability that their mean rebuild time exceeds at 8.7 hours is 0.1459.
The answer in this question is 0.1459